Synchronization of stochastic complex networks with time delay via feedback control based on discrete-time state observations

In this paper, synchronization of stochastic complex networks (SCNs) with time delay is researched. A feedback control method is introduced to drive such SCNs to achieve inner synchronization in mean square. Different from previous researches, the feedback control we designed is based on discrete-time state observations. Moreover, by exploiting Lyapunov method and Kirchhoff's Matrix Tree Theorem in graph theory, some sufficient criteria are obtained to guarantee synchronization in mean square and asymptotical synchronization in mean square of SCNs. What is more, we make use of the theoretical results to analyze asymptotical synchronization in mean square of second-order Kuramoto oscillators with time delay and stochastic disturbances and get a sufficient criterion. At the end of this paper, a numerical example is provided to validate the effectiveness and feasibility of our theoretical results.